Octagar family: Difference between revisions

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 == Octagar ==
-[[Comma]]: 4000/3969
+Subgroup: 2.3.5.7
-[[Mapping]]: [{{val|1 0 1 4}}, {{val|0 1 0 -2}}, {{val|0 0 2 3}}]
+[[Comma list]]: [[4000/3969]]
-Mapping generators: 2, ~3, ~63/40
+[[Mapping]]: [{{val| 1 0 1 4 }}, {{val| 0 1 0 -2 }}, {{val| 0 0 2 3 }}]
-Minimax tuning:
+Mapping generators: ~2, ~3, ~63/40
-* 7-limit minimax:
-: [{{monzo|1 0 0 0}}, {{monzo|5/6 1/3 1/2 -1/3}}, {{monzo|0 0 1 0}}, {{monzo|5/6 -2/3 1/2 2/3}}]
-: [[Eigenmonzo]]s (unchanged intervals): 2, 7/6, 5/4
-* 9-limit minimax:
+[[Mapping to lattice]]: [{{val| 0 -1 -2 -1 }}, {{val| 0 -1 0 2 }}]
-: [{{monzo|1 0 0 0}}, {{monzo|5/8 1/2 3/8 -1/4}}, {{monzo|0 0 1 0}}, {{monzo|5/4 -1 3/4 1/2}}]
-: [[Eigenmonzo]]s (unchanged intervals): 2, 5/4, 9/7
-Lattice basis: 63/50 length = 0.8966, 21/20 length = 1.0605
+Lattice basis:
+: 63/50 length = 0.8966, 21/20 length = 1.0605
+: Angle (63/50, 21/20) = 97.743 degrees
-Angle(63/50, 21/20) = 97.743 cents
+[[Minimax tuning]]:
+* [[7-odd-limit]]
-[[Mapping to lattice]]: [{{val|0 -1 -2 -1}}, {{val|0 -1 0 2}}]
+: [{{monzo| 1 0 0 0 }}, {{monzo| 5/6 1/3 1/2 -1/3 }}, {{monzo| 0 0 1 0 }}, {{monzo| 5/6 -2/3 1/2 2/3 }}]
+: [[Eigenmonzo]]s (unchanged intervals): 2, 7/6, 5/4
+* [[9-odd-limit]]
+: [{{monzo| 1 0 0 0 }}, {{monzo| 5/8 1/2 3/8 -1/4 }}, {{monzo| 0 0 1 0 }}, {{monzo| 5/4 -1 3/4 1/2 }}]
+: [[Eigenmonzo]]s (unchanged intervals): 2, 5/4, 9/7
 {{Val list|legend=1| 12, 26, 27, 41, 53, 94, 121, 162, 189, 215, 230 }}
-[[Badness]]: 0.000216
+[[Badness]]: 0.216 × 10<sup>-3</sup>
 [[Projection pair]]s: 5 - 3969/800, 7 - 27783/4000 to 2.3.7/5
-;[[Hobbits|Hobbit bases]]
+{{Databox|[[Hobbit|Hobbit bases]]|
 .3.7/5 subgroup
+* 12: 50/49, 256000/250047
+* 15: 256000/250047, 1029/1000
+* 23: 12800000/12252303, 107163/102400
+}}
-: 50/49, 256000/250047
+== Nakika ==
+Subgroup: 2.3.5.7.11
-: 256000/250047, 1029/1000
-: 12800000/12252303, 107163/102400
-=== Nakika ===
 [[Comma list]]: 100/99, 245/242
-Mapping: [{{val|1 0 1 4 4}}, {{val|0 1 0 -2 -2}}, {{val|0 0 2 3 4}}]
+[[Mapping]]: [{{val| 1 0 1 4 4 }}, {{val| 0 1 0 -2 -2 }}, {{val| 0 0 2 3 4 }}]
-Mapping generators: 2, ~3, ~11/7
+Mapping to lattice: [{{val| 0 1 2 1 2 }}, {{val| 0 -1 0 2 2 }}]
-Associated linear temperament: [[Tetracot family|octacot]]
+Lattice basis:
+: 11/7 length = 0.798, 22/21 length = 0.906
+: Angle (11/7, 22/21) = 97.747 degrees
-Lattice basis: 11/7 length = 0.798, 22/21 length = 0.906
+{{Val list|legend=1| 12, 15, 26, 29, 41 }}
-Angle(11/7, 22/21) = 97.747 degrees
+[[Badness]]: 0.539 × 10<sup>-3</sup>
-Mapping to lattice: [{{val|0 1 2 1 2}}, {{val|0 -1 0 2 2}}]
+[[Projection pair]]s: 5 - 242/49, 7 - 21296/3087, 11 - 234256/21609 to 2.3.11/7
-Vals: {{Val list| 12, 15, 26, 29, 41 }}
+[[Associated temperament]]: [[octacot]]
-Badness: 0.000539
+Scales: [[nakika12]]
-Projection pairs: 5 - 242/49, 7 - 21296/3087, 11 - 234256/21609 to 2.3.11/7
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-Scales: [[nakika12]]
-==== 13-limit ====
 Comma list: 100/99, 105/104, 245/242
-Mapping: [{{val|1 0 1 4 4 2}}, {{val|0 1 0 -2 -2 -1}}, {{val|0 0 2 3 4 5}}]
+Mapping: [{{val| 1 0 1 4 4 2 }}, {{val| 0 1 0 -2 -2 -1 }}, {{val| 0 0 2 3 4 5 }}]
-Mapping generators: 2, ~3, ~11/7
 Vals: {{Val list| 12f, 15, 26, 29, 41 }}
-[[Category:Theory]]
+[[Category:Regular temperament theory]]
 [[Category:Temperament family]]
-[[Category:Octagar]]
+[[Category:Octagar family| ]] <!-- main article -->
 [[Category:Rank 3]]